J 2001

Racines d'unités cyclotomiques et divisibilité du nombre de classes d'un corps abélien réel

GREITHER, Cornelius; Radan KUČERA and Said HACHAMI

Basic information

Original name

Racines d'unités cyclotomiques et divisibilité du nombre de classes d'un corps abélien réel

Name (in English)

Roots of cyclotomic units and divisibility of the class number of real abelian fields

Authors

GREITHER, Cornelius; Radan KUČERA and Said HACHAMI

Edition

Acta Arithmetica, Warszawa, Instytut Matematyczny PAN, 2001, 0065-1036

Other information

Language

French

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Poland

Confidentiality degree

is not subject to a state or trade secret

Impact factor

Impact factor: 0.458

Marked to be transferred to RIV

Yes

RIV identification code

RIV/00216224:14310/01:00003125

Organization unit

Faculty of Science

Keywords in English

cyclotomic units
Changed: 27/6/2007 09:45, prof. RNDr. Radan Kučera, DSc.

Abstract

In the original language

Le nombre de classes $h_K$ d'un corps abélien reél $K$ a la réputation d'etre difficile a calculer, et pour cause. Dans ce travail, $K$ est un corps de gendres de type $(p,...,p)$ ($l$ fois $p$, $p$ est un premier impair). Notre résultat principal affirme que $h_K$ est divisible par $p^{2^l-l^2+l-2}$.

In English

The class number $h_K$ of a real abelian field $K$ is known to be difficult to compute. In the paper, $K$ is a genus field of the type $(p,...,p)$ ($l$ times $p$, $p$ is an odd prime). Our main result states that $h_K$ is divisible by $p^{2^l-l^2+l-2}$.

Links

MSM 143100009, plan (intention)
Name: Matematické struktury algebry a geometrie
Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures of algebra and geometry